The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar

Abstract

In this note, we show that the strong Viterbo conjecture holds true on any convex toric domain, and that the Viterbo's volume-capacity conjecture holds for the product of a $1$-unconditional convex body $A\subset {\mathbb{R}}^n$ and its polar. We also give a direct calculus proof of the symmetric Mahler conjecture for $l_p$-balls.

Latex, 14 pages, the title is changed, add new results and references

References in corpus (2)

• When symplectic topology meets Banach space geometry
• Symplectic embeddings of the ${\ell }_p$-sum of two discs